Simplify the following expression: $t = \dfrac{z^2 + 2z - 48}{z + 8} $
First factor the polynomial in the numerator. $ z^2 + 2z - 48 = (z + 8)(z - 6) $ So we can rewrite the expression as: $t = \dfrac{(z + 8)(z - 6)}{z + 8} $ We can divide the numerator and denominator by $(z + 8)$ on condition that $z \neq -8$ Therefore $t = z - 6; z \neq -8$